302 HENRY H. DONALDSON 



times. We may infer, therefore, that the change in proportion 

 takes place during the period of rapid growth preceding puberty. 



This is the period of calcification, and it seems most probable 

 that the change in form accompanies the change in material, as 

 the bones pass from a state of cartilage, a comparatively weak 

 material, to that of the completely ossified bone, which is remark- 

 ably strong, as well as possessing other mechanical properties 

 that are noteworthy. 



The fact that the long bones at maturity are more slender than 

 at puberty, or earlier, is a result of interest in view of the state- 

 ments made here and there that in order to maintain like struc- 

 tural strength, when enlarged, a bone must show an increase 

 in diameter which is relatively greater than the increase in 

 length. The earliest attempt to state these relations seems to 

 have been made by Galileo (1638). 



On page 130 of the translation of his work by Crew and 

 Salvio (see Galileo) is given a figure showing the computed 

 diameter of a larger bone three times the length of a smaller one. 

 The larger bone there depicted is monstrous. In this case Galileo 

 proceeded on the assumption that the material was the same in 

 both bones — that the dimensions of the smaller bone enabled it to 

 just resisting breaking when supported at one end — and that the 

 strength of the larger bone, when so determined, was equal to 

 that of the smaller. 



On these assumptions his conclusion is .valid and the dimen- 

 sions shown are justified, but the selection of bones to illustrate 

 these relations was unfortunate and misleading because osseous 

 tissue has qualities quite different from those which were assumed 

 for the argument. 



The data presented have two different uses; one, to show the 

 manner in which the weight and length of the various parts of 

 the skeleton increase, and the other, to give a series of values 

 to which subsequent observations can be referred for comparison. 



A word of comment on this second use is in order. Despite the 

 fact that the bones are so dense and give so direct an impression 

 of immutability, yet a moment's consideration serves to make it 

 plain that like the other systems of the body the osseous system 



